Can you survive the constructed response arena?

What are we going to learn today?  Using topical literature to teach mathematical processes. Specifically: Constructed response / performance task.  Even the lowest students can complete the highest rigor.

Why should we combine math & literacy?  All 50 states have some form of constructed response questions on their elementary school NCLB test.  While not explicitly mentioning constructed response, the CCSS lays out a framework lending to this type of questioning/instruction.

What are the Common Core Standards?  Third Grade: 3.OA.3-1: Use multiplication within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.  Fourth Grade: 4.OA.2: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 4.OA.3: Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.  Fifth Grade: 5.OA.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Common – Common Core Standards  All grades 3-5: SMP#1: Make sense of problems and persevere in solving them. SMP#2: Reason abstractly and quantitatively. SMP#3: Construct viable arguments and critique the reasoning of others. SMP#4: Model with mathematics. SMP#5: Use appropriate tools strategically. SMP#6: Attend to precision. SMP#7: Look for and make use of structure. SMP#8: Look for and express regularity in repeated reasoning.

Why The Hunger Games?  Level II book – math understanding enhances the literacy understanding.  Interest among students (and teachers).  Flexibility in application of the program.  Ability for differentiation. Whole group / small group / collaborative learning. Cross grade level opportunities.  Personalized identification.  Multiple applications beyond math and writing!

How to use The Hunger Games.  Page 13: “You become eligible for the reaping the day you turn twelve. That year, your name is entered once. At thirteen, twice, and so on and so on until you reach the age of eighteen, the final year of eligibility, when your name goes into the pool seven times…but here’s the catch. Say you are poor and starving as we were. You can opt to add your name more times in exchange for tesserae. Each tessera is worth a meager year’s supply of grain and oil for one person. You may do this for each of your family members as well. So, at the age of twelve, I had my name entered four times. Once because I had to and three times for tessarea for grain and oil for myself, Prim, and my mother. In fact, every year I have needed to do this, and the entries are cumulative. So now, at age sixteen, my name will be in the reaping twenty times. Gale, who is eighteen and has either helping or single-handedly feeding a family of five for seven years, will have his name in forty-two times.”

The questions. Developed by Dr. Jeffrey Shih – UNLV  Show why Katniss has 20 entries in the reaping this year.  Show why Gale has 42 entries in the reaping this year.  If Madge, the mayor’s daughter, is the same age as Katniss (16), how many entries does she have in the reaping this year? Why is her number of entries different from Katniss’ number of entries? Why is Gale not happy with Madge?  Compare the likelihood that Katniss will get picked as opposed to Madge,  What information would we need to have to calculate the probability that Katniss will be picked?  Assume that there are 3,000 paper slips in the girls’ reaping ball. What is the probability that Katniss gets picked? What is the probability that Madge get picked? What is the probability that Prim gets picked?  For each of the probabilities in question 6, find a real world example that is close to each probability.  How many people are in your family? If you had to support all of them, how many entries would you have at ages: 12, 13, 14, 15, 16, 17, and 18?  How many entries does Madge have at each age?  Compare your number of entries with Madge. Is it fair?

Focus on question 1 & 2  Show why Katniss has 20 entries in the reaping this year.  Show why Gale has 42 entries in the reaping this year.  Result is known and the start is known.  The challenge is finding the ‘change unknown’.  Teacher goal: See/hear the explanation. Understand the process.

Lack of instruction.

The constructed response.  Question 1: Show why Katniss has 20 entries in the reaping this year.

The Thought Process  Explanation of thought process is the key.  Students can use any means to find an answer. Algorithms, manipulatives, tally marks, pencil & paper, etc…

The results.

The results. (Gale equation)

The take away.  Literature can be used to excite the students and open the door to mathematical understanding.  Constructed response and performance tasks are the inevitable future of testing.  CCSS value the process.  With true differentiation even the most struggling students can solve the questions with the highest rigor.

Thank you!  Lloyd Goldberg My.CCSD.net/MrG  Ann Moody